Rabbits (prey) graze grass and reproduce; foxes (predators) hunt rabbits to survive and reproduce. This classic Lotka-Volterra system produces cyclic booms and busts: prey grow when predators are scarce, predators then multiply on abundant prey, overhunting crashes the prey population, and starving predators decline — restarting the cycle. A finite carrying capacity (grass/food limit) dampens the oscillations toward a stable equilibrium.
dPrey/dt = a·Prey·(1-Prey/K) - b·Prey·Pred
dPred/dt = c·Prey·Pred - d·Pred
- Prey growth rate (a) — how fast rabbits reproduce absent predation; higher a means bigger population swings.
- Predator efficiency (b) — how effectively foxes convert hunting into predation pressure on rabbits.
- Carrying capacity (K) — the grass-limited ceiling on the rabbit population, which stabilizes the cycle.
- Reset button — restarts both populations from small initial values to observe the boom-bust cycle from scratch.
Wildlife managers use Lotka-Volterra-style models to understand real predator-prey systems like Canada lynx and snowshoe hare population cycles.